The well-known Braess’ paradox illustrates situations when adding a new link to a transport network might not reduce congestion in the network but instead increase it. This is due to individual entities acting selfishly/separately when making their travel plan choices and hence forcing the system as a whole not to operate optimally. Deeper insight into this paradox from the viewpoint of the structure and characteristics of networks may help transport planners to avoid the occurrence of Braess-like situations in real-life networks. A generally accepted belief is that Braess’ paradox is widespread. This was confirmed by some researchers who claimed that the likelihood of the paradox is 50%, or even higher under some assumptions. In this talk, we will discuss our recent results devoted to the probability of Braess' paradox to occur in the classical network configuration introduced by Braess.